My dh was the assistant director of a family practice medical residency program for many years. He was very closely involved with their training and education, and had exposure to many residents over the years. (These would be medical school graduates, doing their 3 year residency to become family practice physicians.) I told him about this thread, and asked him his opinion of the residents' overall writing skills.
Although he rarely saw anything they actually wrote, he estimates that about 70% had poor writing skills, based on their dictations in the patients' charts.
I would have guessed about half, but he says it was much worse than that.
I think the people that really rise to the top of their profession (program directors, administrators, professors, etc.) would certainly need to excel at writing. But for the majority, good writing skills are optimal and desirable, but uncommon and not absolutely necessary.